Which country produces the biggest share of America’s flat-screen TVs? You know it can’t be China, or we wouldn’t bother asking.

Three years ago, a Pentagon report warned that Mexico was on the brink of becoming a failed state, notes a special report in The Economist. Instead, Mexico’s economic growth has overtaken and surpassed that of Brazil. And as Chinese wages have quintupled in the past 10 years, Mexico’s competitiveness is rising to match its great field position next door to the US Sun Belt. The flat-screen TVs are the least of it. What’s amazing to The Economist is how little Americans know about the progress of their southern neighbor. It estimates that nearly a tenth of current US residents, or their children, are Mexican citizens. But as the Monitor has noted, net migration from Mexico has dropped to zero or lower as opportunities there have expanded.

Many Americans have heard, if vaguely, of Mayan calendars that seem to predict the end of the world coming in a few weeks. But few have heard that recent translations revise that apocalypse into something more like a renewal or fresh start. And that, the magazine argues, looks to be where Mexico is heading.

Lincoln’s example for today’s mess

In these times of winter winds whipping across the “fiscal cliff” at Americans’ feet, compromise is suddenly in again. What was scorned in the tea party upswell of 2010 as caving in to bad Washington habits, is lauded in late 2012 as adult behavior and getting something done.

History, of course, stands on both sides of the compromise question. Abraham Lincoln may have been the self-effacing pragmatist who could hold together a diverse “team of rivals.” But he was not about compromise. This is something the new Steven Spielberg film on Lincoln gets right, says The New Yorker’s Adam Gopnik. The United States had been straddling various compromises over slavery for years, he says, and there are still arguments over whether Lincoln could have avoided the unprecedented human suffering of the war. But Lincoln instead stood at the end of the line for compromise. His position was absolute, both on union and on slavery.

“Lincoln was an uncompromising man who sponsored violence on a hitherto unimaginable scale; that he paid the highest price himself for the noble but hugely costly morality in which he believed is one of the things that makes his story still so fateful and, in its way, uncompromised.”

Standing strong and unbending against all foreign adversaries is one of the lessons generations of Americans have drawn from President Kennedy’s “eyeball to eyeball” showdown with Nikita Khrushchev in the Cuban missile crisis 50 years ago. Kennedy’s threat to strike at those missiles risked a nuclear escalation of holocaust proportions. (There is also a movie version, “Thirteen Days,” with Kevin Costner.)

The Soviets blinked first and withdrew the missiles. Lesson learned. But Leslie Gelb, a foreign-policy expert who was in the State Department at the time, argues in Foreign Policy magazine that Americans learned the wrong lesson. They have ignored, played down, or forgotten that Kennedy didn’t just stand down his superpower rival; he worked a deal. His bargain for a missile withdrawal was not only that he promised not to invade Cuba, but that the US withdraw its Jupiter missiles from Turkey. Part of the deal, Mr. Gelb writes, was that the Soviets wouldn’t mention the Jupiter withdrawal. They didn’t. And the real-leaders-don’t-bargain-with-the-enemy narrative is the one that stuck.

New facts, faded facts, and former facts

These days, not only is there far too much to know, but much of it isn’t true. Some facts actually change over time: The summit of Mt. Everest shifts a few centimeters each year, for example. And some facts – many, it appears – turn out to be not so factual. The Half-life of Facts: Why Everything We Know Has an Expiration Date, a book by Harvard-affiliated applied mathematician Samuel Arbesman, finds overarching patterns in scientific findings and conclusions.

Note first that of all the scientists in human history, a majority are alive and working today. By 1960, mathematician Derek J. da Solla Price concluded that scientific knowledge was doubling every 15 years.

But Dr. Arbesman notes another trend: the decay of what we formerly thought were facts. A review of medical research on liver disease found that it took 45 years for half of it to be proved false or otherwise obsolete. And the discredited share kept growing after that. Another study in 2011 found that of 53 landmark cancer research papers, the conclusions of only six could be reproduced in further research.

Everyone who’s seen Popeye cartoons knows the virtues of spinach. It turns out that the fabulous iron content of spinach is an artifact of a misplaced decimal point by a German chemist in 1870. The mistake was discovered in the 1930s, but spinach’s reputation remains unsullied in the popular mind.The problem, writes Arbesman, is that “we persist in only adding facts to our personal store of knowledge that jibe with what we already know, rather than assimilate new facts irrespective of how they fit our worldview.”